A289393 - OEIS

%I #12 Jul 08 2017 06:50:02

%S 1,-18,-108,-936,-13194,-224424,-4218264,-84318336,-1759467636,

%T -37903487130,-836893437912,-18844318997496,-431163494289720,

%U -9997357777073064,-234430475682110256,-5550426839122171776,-132513976699508759994

%N Coefficients in expansion of E_2^(3/4).

%H Seiichi Manyama, <a href="/A289393/b289393.txt">Table of n, a(n) for n = 0..703</a>

%F G.f.: Product_{n>=1} (1-q^n)^(3*A289394(n)).

%F a(n) ~ c / (n^(7/4) * r^n), where r = A211342 = 0.03727681029645165815098078565... is the root of the equation Sum_{k>=1} A000203(k) * r^k = 1/24 and c = -0.22385630328806525639758543854251232523806175231599584032442913209... - _Vaclav Kotesovec_, Jul 08 2017

%t nmax = 20; CoefficientList[Series[(1 - 24*Sum[DivisorSigma[1, k]*x^k, {k, 1, nmax}])^(3/4), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 08 2017 *)

%Y E_2^(k/4): A289392 (k=1), A289291 (k=2), this sequence (k=3).

%Y Cf. A006352 (E_2), A289394.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jul 05 2017